Pany Varela scored two goals for Portugal and Angel Claudino was on target for Argentina.
Earlier in the day, Brazil defeated Kazakhstan 4-2 to win a bronze medal.
Portugal captain Ricardinho was named player of the tournament, in what was his ninth major finals, ahead of Pany and Kazakhstan's Douglas Junior.
The 2021 Futsal World Cup was held in Lithuania from September 12 to October 3.